Information theoretic approach to the Perron root of nonnegative irreducible matrices

This paper characterizes the Perron root of nonnegative irreducible matrices in terms of the Kullback Leibler distance (generalized to positive discrete measures). By Perron-Frobenius theory, the Perron root of any nonnegative irreducible matrix is equal to its spectral radius. Thus, the paper establishes a connection between two fundamental concepts of information theory and linear algebra. Moreover, these results are shown to have interesting applications to the classical power control problem in wireless communications networks. Finally, we prove new saddle point characterizations of the Perron root and present possible extensions of the results to more general functions.